From Gibbs' inequality [1]} and Eq. (REF ), one obtains
\(D_{GS}^{(\alpha ,\lambda )}[p\Vert q] &= \int _\mathcal {X} p\ln \frac{p}{m_f^{(\alpha ,\lambda )}(p,q)} d\mu \nonumber \\&\ge \Big (\int _\mathcal {X} p d\mu \Big )\ln \frac{p}{m_f^{(\alpha ,\lambda )}(p,q)} \nonumber \\&\ge 1\cdot \ln 1 = 0. \nonumber \) 

